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Question

Spinel is an important class of oxides consisting of two types of metal ions with the oxide ions arranged in ccp layers. The normal spinel has one-eighth of the tetrahedral holes occupied by one type of metal ion and one-half of the octahedral holes occupied by another type of metal ion. Such a spinel is formed by Mg2+ , Al3+ and O2−. The neutrality of the crystal is being maintained.

If oxide ion is replaced by X−8/3, the number of anionic vacancies per unit cell is :

A
1
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B
2
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C
3
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D
34
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Solution

The correct option is C 1
As O2 ions are at ccp point, spinel has 4 negative ions in its structure and so, the total positive charge should be 8.
However, it has 1 Mg+2 ion occupying one-eight of the tetrahedral holes and 2 Al+3 ions occupying one-half of the octahedral holes. So, the compound is MgAl2O4.

In a unit cell there are 4 O2 having a total charge of 8.
But now,
oxide ion is replaced by X8/3 which should have same total negative charge of 8 for which only 3 X8/3 are required. So, one anionic valency will be present in the modified unit cell.
The formula of the new compound is MgAl2X3.
Option A is correct.

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